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\begin{document}

a)

First recall the various necessary quantities derived from $T_{\mu \nu}$

$$T_{00} = \frac{1}{2} ( E^2 + B^2 )$$
$$T_{0i} = \frac{1}{c} S_i$$
$$T_{ij} = - \left[ E_i E_j + B_i B_j - (E^2 + B^2) \delta_{ij} \right] = - t_{ij}$$

Now apply the product rule to obtain

$$\partial^\alpha L_{\alpha \beta \gamma} = x_\gamma \partial^\alpha T_{\alpha \beta} + T_{\gamma \beta} - x_\beta \partial^\alpha T_{\alpha \gamma} - T_{\beta \gamma} =  x_\gamma \partial^\alpha T_{\alpha \beta} - x_\beta \partial^\alpha T_{\alpha \gamma} $$

where we have used $T_{\alpha \beta} \partial^\alpha x_\gamma = T_{\alpha \beta} \eta^\alpha \, _\gamma = T_{\gamma \beta}$ and the symmetry of $T_{\alpha \beta}$.

setting $\beta, \gamma = i, j$
\begin{eqnarray*}
\partial^\alpha L_{\alpha ij} &=&  x_j \partial^\alpha T_{\alpha i} - x_i \partial^\alpha T_{\alpha j} \\
&=& x_j \partial^0 T_{0 i} + x_j \partial^k T_{k i} - x_i \partial^\alpha T_{\alpha j}
\end{eqnarray*}

Now by the definition of $f_\mu \equiv \partial^\nu T_{\mu \nu}$
$$\partial^\alpha L_{\alpha \beta \gamma} = x_\gamma f_\beta - x_\beta f_\gamma$$
setting $\beta, \gamma = i, j$ and integrating over a 4 dimensional volume
$$\partial^\alpha L_{\alpha i j} = x_j f_i - x_i f_j$$

\end{document}